Long time tail in the diffusion of a spherical polymer

R.B. Jones

Physica A: Statistical Mechanics and its Applications, 1980, vol. 101, issue 2, 389-406

Abstract: We study the velocity autocorrelation function for the diffusion of a spherical macromolecule in solution. The diffusion is described by a generalized Langevin equation with memory character derived previously from fluctuation theory applied to the Debye-Bueche-Brinkman equation which describes the polymer-fluid interaction. The long time behaviour of the velocity autocorrelation function is obtained by establishing a low frequency expansion for the drag coefficient ζ(ω). To derive this expansion we prove a number of analyticity properties of ζ(ω). The longest lived contribution to the velocity autocorrelation function goes as t-32 as first discovered by Alder and Wainwright. We also obtain the first correction term of order t-52 which depends explicitly on the polymer structure. By use of a generalization of the Lorentz reciprocity theorem we show that the coefficient of this t-52 term is given in terms of the polymer mass and the two structure dependent coefficients that enter the static Faxén theorem for the total force on the polymer.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:101:y:1980:i:2:p:389-406

DOI: 10.1016/0378-4371(80)90184-3

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